A plane electromagnetic wave propagating in $$x$$-direction is described by $$E_y = (200 \text{ V m}^{-1}) \sin[1.5 \times 10^7 t - 0.05x]$$. The intensity of the wave is : (Use $$\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}$$)

The intensity of an electromagnetic wave is:

$$I = \frac{1}{2}\epsilon_0 c E_0^2$$

where $$E_0 = 200$$ V/m is the amplitude of the electric field and $$c = 3 \times 10^8$$ m/s.

$$I = \frac{1}{2} \times 8.85 \times 10^{-12} \times 3 \times 10^8 \times (200)^2$$

$$= \frac{1}{2} \times 8.85 \times 10^{-12} \times 3 \times 10^8 \times 4 \times 10^4$$

$$= \frac{1}{2} \times 8.85 \times 3 \times 4 \times 10^{-12+8+4}$$

$$= \frac{1}{2} \times 106.2 \times 10^0$$

$$= 53.1 \text{ W m}^{-2}$$

The answer is $$53.1 \text{ W m}^{-2}$$, which corresponds to Option (2).